OK, I'll explain a bit better, but I'm not familiar with the OEM nav unit as I've never had a car installed with it but I believe it has a seperate amp in the boot that the speakers are powered from. In my instance, the factory non-nav headunit powers the speakers.
The factory amps are a bit lacklustre, so the best improvement is to fit a good aftermarket one. After that, the speakers aren't the best in the world, and 13 years old at this stage, so replacing them with some decent component speakers also yields an improvement. Rear speakers add little to the drivers experience so you can choose to disconnect them or leave them connected but I wouldn't be too bothered about upgrading. The standard door positioning for the front speakers and rear parcelshelf for rear speakers aren't the best for bass so adding a subwoofer is a great improvement.
Adding an amplifier:
The factory e39 headunit has no pre-outs (usual way of connecting an amplifier to a headunit). The way around this is to use an amplifier which can take speaker outputs as inputs i.e. the wire that normally leaves your factory headunit/amp to go to the speaker acts as an input to the new amplifier and then drives the speakers. I used an Alpine MRX-V60 as it had reviewed well and used the speaker line inputs as a trigger to turn on the amp also. You can retain factory wiring to the speakers if you're clever about installation. I mounted the amp in place of the 6CD changer but there are other options.
Changing front speakers for aftermarket components:
This is fairly straight forward and there are loads of guides out there and lots of reviews of what components are best at whatever price point etc.
Adding subwoofer - option 1: factory
The DSP system came with factory subs under parcel shelf as the image shows. They are currently available on eBay for £85 + £25 for the cover.
Installation would be same as OEM method (as well as popping the two pre-cut circles out of parcel shelf), the only modification being to change the connection method - i.e. wire the speakers directly to the amplifier and bypass the standard connector. This is probably the easiest and most OEM solution, with the option to change the subs in the future for an improvement if required.
Adding subwoofer - option 2: aftermarket
You can go 100s of ways for this, but you can get a similar result from above using 2 x 6.5" subs in a custom box mounted in a similar way to factory option. Another popular alternative is to cut out the ski flap and aim the sub through there with a custom box that adds a new false back to the boot, making it a bit shallower.
Hope the above helps, it might be a bit to get your head around now but once you start the job with a bit of research it becomes much simpler.